4x-3y=7 x=13-3y Solve for the variables.

Answer:

The answer is option D.

Step-by-step explanation:

First we must first find the LCM

the LCM of x² - 9 and x + 3 is x² - 9

So we have

[tex] \frac{3}{ {x}^{2} - 9 } + \frac{5}{x + 3} = \frac{3 + 5(x - 3)}{ {x}^{2} - 9} \\ \\ = \frac{3 + 5x - 15}{(x + 3)(x - 3)} \\ \\ = \frac{5x - 12}{(x + 3)(x - 3)} [/tex]

Hope this helps you

Answer:

D

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

Angle AQC, AQB and BQC are 120deg. (360/3=120). Therefore, Angle BZC, CXA and AYB are 60deg. Because, angle BZC is half of angle BQC. same for the other three angles. As, all 3 angles are 60deg, it is an equilateral triangle. So, YZ is 13 therefore as all 3 sides are equal its 13*3=39.

The solution is: 39 is the perimeter of XYZ.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

Angle AQC, AQB and BQC are 120deg.

(360/3=120).

Therefore, Angle BZC, CXA and AYB are 60deg.

Because, angle BZC is half of angle BQC.

same for the other three angles.

As, all 3 angles are 60deg, it is an equilateral triangle.

So, YZ is 13

therefore as all 3 sides are equal

its 13*3=39.

Hence, 39 is the perimeter of XYZ.

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Answer:

B. 3x+15 / 4x+10

Step-by-step explanation:

[tex]\frac{3x+}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex]  -> multiply by the reciprocal

[tex]\frac{3x}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex]  -> reduce the expression

[tex]\frac{3}{2x+5}[/tex] X [tex]\frac{x+5}{2}[/tex] -> multiply the fractions

[tex]\frac{3(x+5)}{2(2x+5)}[/tex]       -> remove parenthesis

and you get:

[tex]\frac{3x+15}{4x+10}[/tex]

-Hope this helps :)

Answer:

The dimensions are x = 23 and y = 23

The maximum area of the rectangle  A = 529

Step-by-step explanation:

Step(i):-

Let given function area of the rectangle

                                    A = x y ....(i)

Given Perimeter of rectangle

                          2 ( x + y ) = 92

                               (x +y ) = 46

                                y = 46 - x ....(ii)

Substitute y = 46 - x in equation (i)

                             A = x (46 - x)

                            A = 46 x - x²  ....(iii)

Differentiating equation (iii) with respective to 'x'

                            [tex]\frac{dA}{dx} = 46(1) - 2 x[/tex]  ...(iv)

Step(ii):-

              [tex]\frac{dA}{dx} = 46(1) - 2 x = 0[/tex]

                       46 - 2 x = 0

                             46  = 2 x

                              x  = 23

Again Differentiating equation (iv) with respective to 'x'

                      [tex]\frac{d^{2} A}{dx^{2} } = - 2 (1) = -2 < 0[/tex]

The maximum value at x = 23

Step(iii):-

From(ii)

                      y = 46 - x

                     y   = 46 - 23

                   y    = 2 3

The dimensions are x = 23 and y = 23

Final answer :-

The dimensions are x = 23 and y = 23

The maximum area of the rectangle

                        A = x y

                      A = 23 ×23

                     A = 529

The maximum area of the rectangle  = 529

The dimension of the rectangle with perimeter 92 m whose area is as large as possible is 23m by 23m

If the perimeter of a rectangle is 92m, hence;

2(x+y) = 92

x is the length

y is the width

x + y = 46 ....... 1

If the area is as large as possible, hence;

xy = maximum .........2

From equation 1, x = 46 - y

Substitute into the second equation

(46-y)y = P(y)

P(y) = 46y - y²

If the product is at the maximum, hence;

dP/dy = 46 - 2y = 0

46 - 2y = 0]

2y = 46

y = 23

Since x + y = 46

x = 46 - y

x = 46 - 23

x = 23

Hence the dimension of the rectangle with perimeter 92 m whose area is as large as possible is 23m by 23m

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Answer:

see below

Step-by-step explanation:

9 x 8 = (10 x 8) - ( blank x 8) =80 - blank = blank

We are replacing 9 with 10 minus something

9 = 10 -1

9 x 8 = (10 x 8) - ( 1 x 8)

           80 - 8

             72

Answer:

$2,160 is what he need for both daughters for 1 year

Step-by-step explanation:

90 x 2 = 180

180 x 12 = 2,160

Dominic need to budget a total of 2160 for a year of gymnastics for both daughters.

Multiplication is one of the basic mathematical operations which includes a number added repeatedly to times of the other number. The final answer is called the product of the numbers.

Multiplication is usually denoted as '×' sign.

a × b indicates that a is added repeatedly upto b times.

Cost for the gymnastics per month per child = 90

In order to find the cost per month for both daughters, we need to multiply 90 with 2.

Cost for the gymnastics per month for 2 daughters = 2 × 90 = 180

To find the total cost for an year, we need to multiply 180 with 12.

Total cost for the year = 180 × 12 = 2160

Hence the total budget for Dominic to send both the daughter in a year is 260.

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Answer:

The point estimate for p is 0.2043.

Step-by-step explanation:

The point estimate for the population proportion of accidents that involved faulty equipment is the number of acidents which involved faulty equipment divided by the number of accidents surveyed.

In this question:

700 accidents surveyed

143 involved faulty equipment

143/700 = 0.2043

The point estimate for p is 0.2043.

Question:

What is the common ratio between successive terms in the sequence?

27, 9, 3, 1

Answer:

common ratio = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

In a geometric progression, the common ratio, r, is the ratio of a term in the sequence to a preceding term in that same sequence. In other words, the common ratio is found by dividing a term by the term just before it. For example, if the geometric sequence is:

a, b, c, d...

The common ratio is found by any of the following;

r = [tex]\frac{b}{a}[/tex]        ----------(i)

r = [tex]\frac{c}{b}[/tex]        -----------(ii)

r = [tex]\frac{d}{c}[/tex]        ------------(iii)

Any of equations (i) through (iii) will give the common ratio of the sequence.

============================================================

Now, from the question, the given sequence is;

27, 9, 3, 1

To get the common ratio, just divide the second term (9) by the first term (27) i.e

r = [tex]\frac{9}{27}[/tex] = [tex]\frac{1}{3}[/tex]

OR

You can also divide the third term (3) by the second term (9). i.e

r = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]

OR

You can choose to divide the fourth term (1) by the third term (3). i.e

r = [tex]\frac{1}{3}[/tex]

Which ever adjacent terms you choose gives you the same result. Therefore, the common ratio of the given sequence is [tex]\frac{1}{3}[/tex]

x = +7 or -7

a = +3 or -3

x = +19 or -5

n = -5 or -7

p = +4 or -2

x = +11 or +1

a = -11 or -7

k = +16 or 0

m = -1 or 0

r = +6 or +1    

: Answer:

Step-by-step explanation:

|3a|=9

a=3

2- |x–7|=12

For the Negative case we'll use -(x-7)  

For the Positive case we'll use (x-7)  

Solve the Negative Case

     -(x-7) = 12  

 Multiply

     -x+7 = 12  

    rearrange and Add up

     -x = 5  

    Multiply both sides by (-1)

     x = -5  (for negative)

Solve the Positive Case

     (x-7) = 12  

     x = 19  

 Which is the solution for the Positive Case

Wrap up the solution

x=-5             ,x=19

 4- |n+6|=1

The Absolute Value term is |n+6|

 For the Negative case we'll use -(n+6)  

For the Positive case we'll use (n+6)  

Solve the Negative Case

     -(n+6) = 1  

    Multiply

   -n-6 = 1  

  -n = 7  

  Multiply both sides by (-1)

     n = -7  

  Which is the solution for the Negative Case

Solve the Positive Case

     (n+6) = 1  

     n = -5  

Which is the solution for the Positive Case

Wrap up the solution

n=-7

n=-5

5-   |1–p|=3

The Absolute Value term is |-p+1|

 For the Negative case we'll use -(-p+1)  

For the Positive case we'll use (-p+1)  

Solve the Negative Case

     -(-p+1) = 3  

  Multiply

   p-1 = 3  

   Rearrange and Add up

     p = 4  

Solve the Positive Case

     (-p+1) = 3

Rearrange and Add up

   -p = 2  

 Multiply both sides by (-1)

p = -2

Which is the solution for the Positive Case

Wrap up the solution

p=4                             , p=-2

6 - |6–x|=5    

The Absolute Value term is |-x+6|

For the Negative case we'll use -(-x+6)  

For the Positive case we'll use (-x+6)  

Solve the Negative Case

   -(-x+6) = 5  

  Multiply

   x-6 = 5

 Rearrange and Add up

     x = 11  

Solve the Positive Case

     (-x+6) = 5  

 Rearrange and Add up

     -x = -1

  Multiply both sides by (-1)

  x = 1  

   Which is the solution for the Positive Case

Wrap up the solution

x=11              ,   x=1

7-

The Absolute Value term is |a+9|

 For the Negative case we'll use -(a+9)  

For the Positive case we'll use (a+9)  

Solve the Negative Case

     -(a+9) = 2  

  Multiply

     -a-9 = 2  

    Rearrange and Add up

     -a = 11  

  Multiply both sides by (-1)

   a = -11  

   Which is the solution for the Negative Case

Solve the Positive Case

     (a+9) = 2  

    Rearrange and Add up      a = -7  

 Which is the solution for the Positive Case

Wrap up the solution

a=-11    a=-7

8-  |k–8|=8

The Absolute Value term is |k-8|

For the Negative case we'll use -(k-8)  

For the Positive case we'll use (k-8)  

Solve the Negative Case

     -(k-8) = 8  

    Multiply

     -k+8 = 8  

    Rearrange and Add up

     -k = 0  

    Multiply both sides by (-1)

   k = 0  

  Which is the solution for the Negative Case

Solve the Positive Case

     (k-8) = 8  

  Rearrange and Add up

     k = 16  

    Which is the solution for the Positive Case

Wrap up the solution

k=0  k=16

Solutions on the Number Line

Two solutions were found :

k=16

k=0

9-|2m+1|=1

The Absolute Value term is |2m+1|  

For the Negative case we'll use -(2m+1)  

For the Positive case we'll use (2m+1)  

Solve the Negative Case

     -(2m+1) = 1  

    Multiply

     -2m-1 = 1  

Rearrange and Add up

     -2m = 2  

    Divide both sides by 2

     -m = 1  

    Multiply both sides by (-1)

     m = -1  

    Which is the solution for the Negative Case

Solve the Positive Case

     (2m+1) = 1  

Rearrange and Add up

  2m = 0  

  Divide both sides by 2

   m = 0  

 Which is the solution for the Positive Case

Wrap up the solution

m=-1

m=0

Solutions on the Number Line

Two solutions were found :

m=0

m=-1

9- |7–2r|=5

The Absolute Value term is |-2r+7|

For the Negative case we'll use -(-2r+7)  

Solve the Negative Case

     -(-2r+7) = 5  

    Multiply

     2r-7 = 5  

    Rearrange and Add up

     2r = 12  

    Divide both sides by 2

     r = 6  

Solve the Positive Case

     (-2r+7) = 5  

   Rearrange and Add up

   -2r = -2  

  Divide both sides by 2

   -r = -1  

 Multiply both sides by (-1)

   r = 1  

  Which is the solution for the Positive Case

Wrap up the solution

r=6

r=1

Answer:

[tex]\boxed{Larger \ Number = -7}[/tex]

Step-by-step explanation:

Let the consecutive numbers be x and x+1 (Since they are coming one after another)

So, Given Condition is:

x+1 = 9 + 2(x)

x+1 = 9 +2x

Subtracting -2x to both sides

x+1-2x = 9

-x+1 = 9

Subtracting 1 from both sides

-x = 9-1

-x = 8

=> x = -8

The larger number is:

=> x+1 = -8+1 = -7

Answer: 57 degrees

Step-by-step explanation: We can use our knowledge of knowing the sum of the interior angles of a triangle to be 180 degrees, to find the measure of the angle. So we can do 90 degrees plus 33 degrees, and then subtract the sum from 180 to find the measure of the angle. So we get 123 degrees when we add up 90 and 33 and when we subtract 123 degrees from 180 we get, 57 degrees as the answer.

Answer:

57 degrees

Step-by-step explanation:

We can use our knowledge of knowing the sum of the interior angles of a triangle to be 180 degrees, to find the measure of the angle. So we can do 90 degrees plus 33 degrees, and then subtract the sum from 180 to find the measure of the angle. So we get 123 degrees when we add up 90 and 33 and when we subtract 123 degrees from 180 we get, 57 degrees as the answer.

Answer:

7. f⁻⁻¹(x)=x-3                 11. f⁻⁻¹(x)= 2x/(1-x)

Step-by-step explanation:

to find the inverse of an expression:

1. change f(x) to y.

2. switch the x and y values.

3. solve to find y.

So....                                                              

7.) f(x)=x+3                              11.) f(x)=  x/(x+2)

y=x+3                                            y=x/(x+2)

x=y+3                                            x=y/(y+2)

f⁻⁻¹(x)=x-3                                       f⁻⁻¹(x)= 2x/(1-x)

Answer:

Option A.

Step-by-step explanation:

It is given that, sales (in hundreds) for several months can be modeled by the function:

[tex]S(m)=-0.625|m-8|+5[/tex]

We need to find the month in which 400 toys were sold.

Substitute S(m)=4 in the given function.

[tex]4=-0.625|m-8|+5[/tex]

[tex]4-5=-0.625|m-8|[/tex]

[tex]-1=-0.625|m-8|[/tex]

[tex]\dfrac{-1}{-0.625}=|m-8|[/tex]

[tex]1.6=|m-8|[/tex]

Now,

[tex]\pm 1.6=m-8[/tex]

[tex]1.6=m-8[/tex] or [tex]-1.6=m-8[/tex]

[tex]1.6+8=m[/tex] or [tex]-1.6+8=m[/tex]

[tex]9.6=m[/tex] or [tex]6.4=m[/tex]

Approx the value to the next whole number.

[tex]m\approx 10[/tex] or [tex]m\approx 7[/tex]

It means, 400 toys were sold on 7th and 10th month.

Therefore, the correct option is A.

Answer:

6 ounces of red beads

6 ounces of gold beads

Step-by-step explanation:

x + y = 12

x + 3y = 24

We can solve this with substitution or elimination.  In this case, I would suggest elimination.  Subtract the first equation from the second:

2y = 12

y = 6

Plug back into either equation to find x.

x = 6

Answer:

How many ounces of red beads will Juanita buy to break even?

6

How many ounces of gold beads will she buy?

6

Step-by-step explanation:

Because I got 100 percent on EDG 2020

Answer:

correlation can be used to determine the direction of the relationship between two variables may be this is the answer not sure

Answer:

=9/2yd³

Step-by-step explanation:

the surface area of a sphere, radius r

S = 4πr²

9 π = 4 π r 2 ⇒ r 2 = 9 π 4 π = 9 4 ∴ r = √ 9 4 = 3 2

The volume of a sphere is

V=43πr3=43×π×(32)3=4×3×3×33×2×2×2π

=9/2yd³

Answer is =9/2yd³ for this question

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Hope this helps.

Answer:

a) This portfolio loses money in 29.81% of the years.

b) The cutoff for the highest 15% of annual returns with this portfolio is a return of 53.16%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 17.9, \sigma = 34[/tex]

a.) What percent of years does this portfolio lose money, i.e. have a return less than 0%?

We have to find the pvalue of Z when X = 0. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0 - 17.9}{34}[/tex]

[tex]Z = -0.53[/tex]

[tex]Z = -0.53[/tex] has a pvalue of 0.2981

This portfolio loses money in 29.81% of the years.

b.) What is the cutoff for the highest 15% of annual returns with this portfolio?

This is the 100 - 15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.037 = \frac{X - 17.9}{34}[/tex]

[tex]X - 17.9 = 1.037*34[/tex]

[tex]X = 53.16[/tex]

The cutoff for the highest 15% of annual returns with this portfolio is a return of 53.16%.

Answer:

x=9

Step-by-step explanation:

for this sort of a problem, I would set up a proportion

5/25=x/45

multiply both sides by 25 and 45

45*5=x*25

225=25x

x=9

Answer:

Greatest number = 9867

Smallest number = 1027

Step-by-step explanation:

Greatest number:

- - - 7

In order to form the greatest number, we should simply put the greatest available digit at the thousands place, the second greatest at the hundreds place and the third greatest at the tens place (which would be 9, 8, and 6 respectively).

9867

Smallest number:

- - - 7

In order to form the greatest number, we should simply put the lowest available digit at the thousands place (excluding zero since a number can't start with a zero), put zero at the hundreds place and the third lowest at the tens place (which would be 1, 0, and 2 respectively).

1027

Answer:

a.) dx3x² + 2

Use the properties of integrals

That's

integral 3x² + integral 2

= 3x^2+1/3 + 2x + c

= 3x³/3 + 2x + c

= x³ + 2x + C

where C is the constant of integration

b.) x³ + 2x

Use the properties of integrals

That's

integral x³ + integral 2x

= x^3+1/4 + 2x^1+1/2

= x⁴/4 + 2x²/2 + c

= x⁴/4 + x² + C

c.) dx6x 5 + 5

Use the properties of integrals

That's

integral 6x^5 + integral 5

= 6x^5+1/6 + 5x

= 6x^6/6 + 5x

= x^6 + 5x + C

d.) x^6 + 5x

integral x^6 + integral 5x

= x^6+1/7 + 5x^1+1/2

= x^7/7 + 5/2x² + C

Hope this helps

Answer:

The answer is 24x-42.

Step-by-step explanation:

here, the given expression is 6(4x-7)

= 24x- 42... is simplified form of equation.

hope it helps

Answer:

Tan B = 24/10 = 12/5

Step-by-step explanation:

Tangent is opposite/adjacent. The side opposite of B is 24 and adjacent to that is 10.

It is D.

you must multiply the second equation by 3, so that the +3y in the first equation can cancel out the (now) -3y in the second equation.

Answer:

  see below

Step-by-step explanation:

It can be useful to remember that the angle θ of rotation between the x-y plane and the x'-y' plane is given by ...

  cot(2θ) = (A -C)/B

where the standard form equation is ...

  Ax² +Bxy +Cy² +Dx +Ey +F = 0

For a 30° rotation, you want ...

  (A -C)/B = cot(2·30°) = 1/√3

Looking at the answer choices, you have ...

  A: (A -C)/B = (3 -(-39))/(42√3) = 1/√3 . . . as required

  B: (A -C)/B = (3 -(-39))/(-12√3) = 7/(2√3)

  C: (A -C)/B = (-39 -3)/(42√3) = -1/√3

  D: AC > 0, not a hyperbola

_____

Based on rotation angle only, the appropriate choice is the first choice. Because the term signs in the x'-y' formula are different, the figure is a hyperbola. In general form, the equation describes a hyperbola when AC<0.

Answer:

the first answer choice is correct!

Step-by-step explanation:

took the test amd got it correct:)) hope this helps:)) have a good day:))

Answer:

595

Step-by-step explanation:

Let the first integer be n. Then each consecutive integer will be (n+1), (n+2)... until (n+16).

First, from the formula [tex]k/2(a+x_{k})[/tex], where k is the number of elements and xk is the last element, we can find 1+2+3 ... +15+16 = (16/2)(1+16)=136.

Anyways, this means that 17n+136=306.

We can find that n=10

Thus, the first integer is 10, and the 17th integer will be 10+16=26.

Thus, the first integer immediately proceeding 26 is 27. There are a total of 17 digits including 27 so we can add 16 to 27 to find the last digit, which is 43. There are again 17 digits in this set.

Thus, we have: 17/2(27+43)=595.

Answer:

A. System of equations:

[tex]3.2C+3P=48.5\\C+P=15.5[/tex]

B. 5.5 pounds of peanut butter fudge were sold.

Step-by-step explanation:

Given:

Cost of chocolate fudge = $3.20

Cost of peanut butter fudge = $3.00

Total pounds sold = 15.5

Total gross profit = $48.50

C is the number of pounds of chocolate fudge sold.

P is the number of pounds of peanut butter fudge sold.

To find:

System of equations and number of pounds of peanut butter fudge sold = ?

Solution:

As per given conditions:

1. [tex]C+P=15.5[/tex]

Gross profit from Chocolate fudge: [tex]3.20 \times C[/tex]

Gross profit from Peanut Butter fudge: [tex]3.00 \times P[/tex]

Total gross profit = [tex]3.20C+3.00P = 48.50[/tex]

So, the system of equations is:

[tex]3.2C+3P=48.5\\C+P=15.5[/tex]

2. To find P.

Let us solve the equations.

Multiply 2nd equation with 3 and subtracting from 1st equation:

[tex]0.2C = 48.5- 3 \times 15.5\\\Rightarrow 0.2C = 48.5- 46.5\\\Rightarrow C = 10\ pounds[/tex]

Putting in 2nd equation:

[tex]10+P=15.5\\\Rightarrow P =5.5\ pounds[/tex]

So, the answer is:

5.5 pounds of peanut butter fudge were sold.

Step-by-step explanation:

There are no choices available, so here is a graph of that equation.  Simply compare it to the answer.

Answer:

1. A resposta é a opção C.

2. ( a +b )² = a² + 2ab + b² Verdade

( a - b )² = a² - 2ab + b² Verdade

( a + b ) .( a – b) = a² + b² Falso

( a +b)³ = a³ + 3a²b + 3ab² + b³ Verdade

( a -b)³ = a³ - 3a²b + 3ab² - b³ Verdade

3. a.) m² - 14am + 49a² = ( m - 7a)²

b) m2 – 9n² = m² - (3n)² = (m + 3n)(m - 3n)

c) 30+ 5xy + 12a +2axy = (6 + xy)(5 + 2a)

d) 8a²b + 10ab² = 2ab( 4a + 5b)

Espero que isso ajude você